In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are usi...In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.展开更多
A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemen...A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.展开更多
The paper is to introduce a computational methodology that is based on ordinary differential equations （ODE） solver for the structural systems adopted by a super tall building in its preliminary design stage so as t...The paper is to introduce a computational methodology that is based on ordinary differential equations （ODE） solver for the structural systems adopted by a super tall building in its preliminary design stage so as to facilitate the designers to adjust the dynamic properties of the adopted structural system. The construction of the study is composed by following aspects. The first aspect is the modelling of a structural system. As a typical example, a mega frame-core-tube structural system adopted by some famous super tall buildings such as Taipei 101 building, Shanghai World financial center, is employed to demonstrate the modelling of a computational model. The second aspect is the establishment of motion equations constituted by a group of ordinary differential equations for the analyses of free vibration and resonant response. The solutions of the motion equations （that constitutes the third aspect） resorted to ODE-solver technique. Finally, some valuable conclusions are summarized.展开更多
Keats's poems are famous for beauty,and Ode to Autumn is generally regarded as one of his most beautiful poems.In this ode,Keats presents a vivid picture of the harvesting autumn,in which many forms of beauty can ...Keats's poems are famous for beauty,and Ode to Autumn is generally regarded as one of his most beautiful poems.In this ode,Keats presents a vivid picture of the harvesting autumn,in which many forms of beauty can be captured.The present paper attempts to conduct an analysis of the beauty in Keats's Ode to Autumn,hopefully it could help readers better understand Keats and his works.展开更多
文摘In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.
文摘A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.
基金Acknowledgment The research work was financially supported both by the Natural Science Foundation of China （51178164） and the Priority Discipline Foundation of Henan Province （507909）.
文摘The paper is to introduce a computational methodology that is based on ordinary differential equations （ODE） solver for the structural systems adopted by a super tall building in its preliminary design stage so as to facilitate the designers to adjust the dynamic properties of the adopted structural system. The construction of the study is composed by following aspects. The first aspect is the modelling of a structural system. As a typical example, a mega frame-core-tube structural system adopted by some famous super tall buildings such as Taipei 101 building, Shanghai World financial center, is employed to demonstrate the modelling of a computational model. The second aspect is the establishment of motion equations constituted by a group of ordinary differential equations for the analyses of free vibration and resonant response. The solutions of the motion equations （that constitutes the third aspect） resorted to ODE-solver technique. Finally, some valuable conclusions are summarized.
文摘Keats's poems are famous for beauty,and Ode to Autumn is generally regarded as one of his most beautiful poems.In this ode,Keats presents a vivid picture of the harvesting autumn,in which many forms of beauty can be captured.The present paper attempts to conduct an analysis of the beauty in Keats's Ode to Autumn,hopefully it could help readers better understand Keats and his works.
